Evolution inequalities with noncoercive <i>w </i>_{λ ₀}-pseudomonotone volterra-type mappings

Abstract

We consider a class of differential-operator inequalities with noncoercive w _{λ 0} -pseudomonotone operators. The problem of the existence of solutions of the Cauchy problem for these inequalities is investigated by using the Dubinsky method. A priori estimates for these solutions and their derivatives are obtained. We give a model example that illustrates the results and generalizations obtained.